The indicator is inspired by John Ehlers' article "Using The Fisher Transform" published in November 2002 in the "Technical Analysis Of Stock & Commodities" magazine.

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The Fisher Transform was presented by John Ehlers in the Stocks and Commodity Magazine November 2002.
John Ehlers wrote an article "Using the Fisher Transform" and introduced a Technical Analysis (TA) indicator called the Fisher Transform or Fish.

Fisher Transform indicator is used to identify price reversals and is based on the assumption that prices behave like a Square Wave and do not follow a Gaussian or Normal distribution. In fact, a Gaussian probability density function (PDF) is a bell-shaped curve where 68% of the samples are within one Standard Deviation from the Mean; this is Clearly not true.

The Fisher Transform formula transforms the probability density function of any Waveform to a function that has almost a Gaussian PDF.

It assumes that price distributions behave like Square Waves. The Fisher Transform uses the Mid-point or Median price in a series of calculations to produce an oscillator. A Signal line which is a Previous value of itself is also displayed.

Many trading systems are designed using the assumption that the probability distribution of prices have a Normal, or Gaussian,
Probability Distribution about the mean. In fact, nothing could be farther from the truth. This paper describes how the Fisher Transform converts data to have nearly a Normal Probability Distribution. Given the Probability Distribution is Normal after applying the Fisher Transform, the data is used to create Entry Points with Surgical precision.

Hilbert Transform from John Ehlers book "Cybernetic Analysis for Stocks and Futures"

In mathematics and in signal processing, the Hilbert transform is a Linear Operator that takes a function, u(t), and produces a function, H(u)(t), with the same domain. The Hilbert Transform is important in Signal Processing, where it derives the Analytic representation of a signal u(t).

The Sine Wave (also called MESA) indicator is based on the assumption that markets move in Cyclical Patterns.

Sine Wave indicator was developed in 1996 by the American analyst John Ehlers, who called it a “Trend oscillator”. It is based on the idea of the Economical processes periodicity: the indicator detects this periodicity violations.

The MESA Sine Wave utilizes 2 sine plots to depict if the Market is in a Trend mode or in a Cycle mode.

One line depicts the Sine of the calculated phase angle over time. The other line depicts the Sine of the phase angle advanced by 45 degrees, which is called the Lead Sine. The crossings of the Sine and Lead Sine together provide precise and advanced picture of Cycle mode turning points.

They call it a Trend mode if the plots start to wander the Market.
The Market is in the cycling mode if the 2 plots look like a Sine wave the Market.
In a Trend mode, the Sine and Lead Sine plots typically weaken in a sideways pattern around the Zero-point, running distant and parallel from each other.

The indicator acts in a Completely opposite way comparing to the Adaptive Moving Averages during a Trend Market: in case of a definite trend, Both indicator Lines (Lead Sine and Sine Wave) move parallel to each other and show the Trend direction by their location relative to each other; in case of a flat, the Sine Wave indicator quickly reacts on the Market swing movements. That is one of a few indicators that can be used both during a Trend Market and a Flat and it shows accurate results in either case.

Sine Wave indicator is that it will anticipate Cycle mode turning points rather than waiting for Confirmation (as the majority of Oscillators do).
It is an extremely helpful trait. The indicator also has an extra-advantage that allows the Trend mode whipsaw signals to be minimized.

If the Sine plot crosses below the Lead Sine plot, the Sell signal is sent. A purchase signal is sent as the Sine plot crosses over the Lead Sine plot if the market is in Cycle mode. It is worth trading the Trend if the Market is in the Trend mode. Main Moving Average crossovers are often helpful for exiting and entering positions in this type of market.

This indicator tries to determine the Current phase of the Cycle you are in, has an Advantage over other oscillators such as RSI and Stochastic because it predicts rather than waits for confirmation. Sine Wave gives entry and exit signals 1/16th of a cycle period in advance of the cycle turning point and seldom gives False whipsaw signals when the Market is in a Trend mode.

The Sine Wave (also called MESA) indicator is based on the assumption that markets move in Cyclical Patterns.

Sine Wave indicator was developed in 1996 by the American analyst John Ehlers, who called it a “Trend oscillator”. It is based on the idea of the Economical processes periodicity: the indicator detects this periodicity violations.

The MESA Sine Wave utilizes 2 sine plots to depict if the Market is in a Trend mode or in a Cycle mode.

One line depicts the Sine of the calculated phase angle over time. The other line depicts the Sine of the phase angle advanced by 45 degrees, which is called the Lead Sine. The crossings of the Sine and Lead Sine together provide precise and advanced picture of Cycle mode turning points.

They call it a Trend mode if the plots start to wander the Market.
The Market is in the cycling mode if the 2 plots look like a Sine wave the Market.
In a Trend mode, the Sine and Lead Sine plots typically weaken in a sideways pattern around the Zero-point, running distant and parallel from each other.

The indicator acts in a Completely opposite way comparing to the Adaptive Moving Averages during a Trend Market: in case of a definite trend, Both indicator Lines (Lead Sine and Sine Wave) move parallel to each other and show the Trend direction by their location relative to each other; in case of a flat, the Sine Wave indicator quickly reacts on the Market swing movements. That is one of a few indicators that can be used both during a Trend Market and a Flat and it shows accurate results in either case.

Sine Wave indicator is that it will anticipate Cycle mode turning points rather than waiting for Confirmation (as the majority of Oscillators do).
It is an extremely helpful trait. The indicator also has an extra-advantage that allows the Trend mode whipsaw signals to be minimized.

If the Sine plot crosses below the Lead Sine plot, the Sell signal is sent. A purchase signal is sent as the Sine plot crosses over the Lead Sine plot if the market is in Cycle mode. It is worth trading the Trend if the Market is in the Trend mode. Main Moving Average crossovers are often helpful for exiting and entering positions in this type of market.

This indicator tries to determine the Current phase of the Cycle you are in, has an Advantage over other oscillators such as RSI and Stochastic because it predicts rather than waits for confirmation. Sine Wave gives entry and exit signals 1/16th of a cycle period in advance of the cycle turning point and seldom gives False whipsaw signals when the Market is in a Trend mode.